Pressure
Discussion
definition
Pressure is the ratio of force applied to the area covered…
| P = | F |
| A |
The unit of pressure is the pascal
| ⎡ ⎢ ⎣ |
Pa = | N | = | kg m/s2 | = | kg | ⎤ ⎥ ⎦ |
| m2 | m2 | m s2 |
The pascal is also a unit of stress and the topics of pressure and stress are connected.
- Bed of nails (not really pressure but shear strain, which has the same units)
- Finger bones are flat on the gripping side to increase surface area in contact and thus reduce compressional stresses
gauge vs. absolute
spring loaded pressure gauge
| atm | kPa | device, event, phenomenon, process |
|---|---|---|
| 200 | 20,000 | pressurized breathing apparatus |
| 140 | 14,000 | milk homogenization |
| 110 | 11,000 | rupture compression strength of vertebral disks |
| 7–14 | 700–1400 | puffed cereal manufacture |
| 9 | 900 | espresso machine |
| 4–7 | 400–700 | bicycle tire |
| >4 | >400 | oxygen poisoning and nitrogen narcosis for dives > 30 m |
| 2.7–4.1 | 275–415 | champagne at serving temperature (10 °C) |
| 2.7 | 275 | carbonated soft drinks |
| 2.0–2.5 | 200–250 | car tire |
| >4 | >400 | blast wave, 100% lethality |
| 2.3–4.0 | 230–400 | blast wave, 50% lethality |
| 1.6–2.3 | 160–230 | blast wave, 1% lethality |
| 1.02 | 103 | typical household pressure cooker |
| 1 | 101.325 | one standard atmosphere over environment |
| 47 | bottom of feet while standing | |
| 20 | lungs, extreme exhalation | |
| 17 | sustained pressure, eardrum ruptures | |
| 8 | sustained pressure, eardrum senses pain | |
| 13–19 | blood pressure, arterial, systolic (during a heartbeat) | |
| 8–12 | blood pressure, arterial, diastolic (between heartbeats) | |
| 7–14 | aircraft shock wave | |
| 8.8 | blowing your nose | |
| 11 | eye, severe glaucoma | |
| 1.6–3.0 | eye, normal | |
| 7 | tennis ball | |
| 4.0 | blood pressure, capillary, arterial end | |
| 1.3 | blood pressure, capillary, venous end | |
| 15 | bladder, voiding, maximum | |
| 3 | bladder, micturition reflex (gotta go urge) | |
| 2–4 | bladder, voiding, sustained | |
| 1.3–2.6 | gastrointestinal tract | |
| 0.6–1.6 | cerebrospinal fluid | |
| 0.4–0.9 | blood pressure, venous | |
| 0.6–0.8 | interstitial fluid (osmotic pressure) | |
| 2 | acoustic pressure, eardrum ruptures (160 dB) | |
| 0.02 | acoustic pressure, eardrum senses pain (120 dB) | |
| 2 × 10−8 | acoustic pressure, threshold of hearing (0 dB) | |
| 0 | 0 | environmental pressure |
| −1.3 | lungs, resting | |
| −1.5 | lungs, drinking through a 15 cm straw | |
| −25 | lungs, extreme inhalation | |
| −1 | −101.325 | one standard atmosphere below environment, a perfect vacuum in a standard atmosphere |
| atm | Pa | device, event, phenomenon, process |
|---|---|---|
| 3.4 × 1011 | 3.4 × 1016 | center of the Sun |
| ???? | ???? | center of Jupiter |
| 1010 | 1015 | diamond anvil, record high |
| 3.6 × 106 | 3.6 × 1011 | center of Earth |
| 1,080 | 1.1 × 108 | Marianas Trench, Pacific Ocean (−10,924 m) |
| 160 | 1.6 × 107 | Lake Baikal, Asia (−1,620 m) |
| 140 | 1.4 × 107 | Lake Tanganyika, Africa (−1,470 m) |
| 90 | 9.0 × 106 | surface of Venus |
| 40 | 4.0 × 106 | Lake Superior, North America (−406 m) |
| ???? | ???? | record dive by a human |
| 26 | 2.6 × 106 | helium freezes at about 1 K |
| >3 | >300,000 | oxygen poisoning and nitrogen narcosis for dives > 30 m |
| 108,380 | Earth atmosphere, record high, altitude adjusted (Siberia, 1968) | |
| 106,000 | Earth atmosphere, Dead Sea (−400 m) | |
| 1 | 101,325 | Earth atmosphere, sea level, standard atmosphere |
| 90,000 | Earth atmosphere at 1,000 m, interior of Concorde | |
| 87,000 | Earth atmosphere, record low, altitude adjusted (Typhoon Tip, 1979) | |
| 80,000 | Earth atmosphere at 2,000 m, interior of commercial jet aircraft | |
| 65,000 | Earth atmosphere, La Paz, Bolivia (3,650 m) | |
| ~½ | 53,000 | Earth atmosphere, highest permanently inhabited town (5,100 m) |
| ~40,000~ | Earth atmosphere, vertical limit of human survivability (~7,000 m) | |
| ~⅓ | 31,000 | Earth atmosphere, Mount Everest (8,848 m) |
| ~⅕ | 19,000 | Earth atmosphere, altitude of commercial jet aircraft (12,000 m) |
| 0.063 | 6,400 | Earth atmosphere, Armstrong limit, exposed body liquids boil (19,000 m) |
| >0.033 | >3,300> | low vacuum (LV) |
| <0.033 | <3,300< | medium vacuum (MV) |
| 0.025 | 2,200 | Earth atmosphere, altitude of reconnaissance plane (26,000 m) |
| 0.007 | 700 | surface of Mars |
| 0.002 | 230 | Earth atmosphere, altitude of highest sky dive (41,422 m) |
| 0.0006 | 60 | Earth atmosphere, altitude of highest unmanned balloon flight (52,000 m) |
| ~10−5 | ~1 | surface of Pluto, maximum |
| <10−6 | <0.1 | high vacuum (HV) |
| <10−9 | <10−4 | very high vacuum (VHV) |
| <10−12 | <10−7 | ultra high vacuum (UHV) |
| ~10−13 | ~10−8 | surface of the Moon, daytime |
| ~10−15 | ~10−10 | surface of the Moon, nighttime |
| <10−15 | <10−10 | extreme ultrahigh vacuum (XHV) |
| ~10−17 | ~10−12 | I am told that below this value all vacuum equipment leaks |
the atmosphere
Standard Atmospheric Tables
| gas | formula | molecular weight (g/mol) |
fraction |
|---|---|---|---|
| nitrogen | N2 | 028.0134000 | 0.780840000 |
| oxygen | O2 | 031.9988000 | 0.209476000 |
| argon | Ar | 039.9480000 | 0.009340000 |
| carbon dioxide | CO2 | 044.0099500 | 0.000314000 |
| neon | Ne | 020.1830000 | 0.000018180 |
| helium | He | 004.0026000 | 0.000005240 |
| methane | CH4 | 016.0430300 | 0.000002000 |
| krypton | Kr | 083.8000000 | 0.000001140 |
| hydrogen | H2 | 002.0159400 | 0.000000500 |
| xenon | Xe | 131.3000000 | 0.000000087 |
| overall | 028.9644253 | 0.999997147 |
fluids
The gauge pressure in a uniform fluid at a particular depth is directly proportional to…
- the density of the fluid (ρ). The denser the fluid, the greater the pressure.
- the acceleration due to gravity (g). The stronger the gravity, the greater the pressure.
- the depth (h). The deeper you go, the greater the pressure.
Combining these factors gives the gauge pressure (Pg) at any depth…
Pg = ρgh
Adding on the the surface pressure (P0) gives the absolute pressure…
P = P0 + ρgh
The absolute pressure in a uniform or nonuniform fluid at a particular depth (h) measured along the vertical axis (z) is given by…
| h | ||
| P = P0 + | ⌠ ⌡ | ρ(z)g(z) dz |
| 0 |
Pressure in a uniform fluid — Stevin's law. Simon Stevin (1548–1620) discovered the hydrostatic paradox that the downward pressure of a liquid is independent of the shape of the vessel, and depends only on its height. Stevin was probably the first to work with the concept of pressure, having lived entirely before Pascal or Bernoulli. Stevin's Flemish word for pressure was the noun gheprang from the verb pranghen, to press (geprang and prangen in modern spelling). The current Dutch word for pressure is druk and the verb to press is drukken.
devices
barometer
barometer, manometer, Hare's apparatus
The atmosphere as a unit.
| 1 atm | = 101,325 Pa | (by definition) |
| = 760 torr | (by definition) | |
| = 763.43… mm Hg | (approximately) | |
| = 1.03… kg/cm2 | (approximately) | |
| = 10.3… tonnes/m2 | (approximately) | |
| = 14.7… psi | (approximately) | |
| = 1.06… tons/ft2 | (approximately) |
physiology
blood pressure
ear pressure in the middle ear: eardrum at end of outer ear connected to smaller oval window at beginning of inner ear. 15-30 times greater pressure. combination of difference in membrane diameters and lever effects of middle ear bones.
eye pressure and glaucoma
| location | systolic | diastolic | mean |
|---|---|---|---|
| aorta | 120 | 80 | 100 |
| left ventricle | 120 | 8 | |
| left atrium | 7 | 10 | 4 |
| pulmonay artery | 15 | 7 | 12 |
| right ventricle | 15 | 2 | |
| right atrium | 4 | 4 | 0 |
| pulmonary capillary wedge | 7 | 10 | 4 |
pascal's principle
- Pascal's principle: Pressure changes applied to the surface of an enclosed fluid are transmitted evenly throughout the fluid.
- Water seeks its own level. That's one of the realities of life.
- hydraulics
- Queckenstedt's maneuver - barbaric medical test from the early 20th century to test for spinal stenosis